Line shapes of the Na/K resonance line profiles perturbed by H2 at extreme density

TL;DR

This work tackles the challenge of accurately modeling collision-broadened Na and K resonance lines perturbed by molecular hydrogen in dense astrophysical environments, such as brown dwarfs and exoplanets. It employs a unified line-shape theory based on the Fourier transform of the autocorrelation function, using ab initio Na–H$_2$ and K–H$_2$ potentials to compute profiles from the line core to far wings across densities from $1\times10^{21}$ to $2\times10^{22}$ cm$^{-3}$ at $T=1000$ K. The results reveal that profiles become strongly non-Lorentzian and develop quasi-molecular satellites, with wing absorption exceeding Lorentzian predictions and profile shifts toward satellite frequencies as density increases; the Lorentzian approximation breaks down well before extremely high perturber densities. These findings significantly improve opacity calculations in dense planetary and brown dwarf atmospheres and provide publicly accessible data for model atmosphere codes and spectral synthesis.

Abstract

Collision broadening by molecular hydrogen of sodium and potassium is one of the major broadening mechanisms in the atmospheres of brown dwarf stars and exoplanets at an effective temperature of about 1000K. The accurate computation of line profiles from collision broadening at high density requires use of a Fourier transform of the autocorrelation function inside the model atmosphere code. We strongly warn that use of Lorentzian profiles at a high perturber density neglects radiation during close collisions and may lead to erroneous conclusions.

Figures (4)

• Figure 1: Absorption cross section, $\sigma$, of the $D$2 component of the resonance lines of Na (blue curve) and K (red curve) perturbed by H$_2$ collisions at $T = 1000$ K and $n_{\mathrm{H}_2} = 10^{22}$ cm$^{-3}$. The Lorentzian approximation is overplotted for comparison (dashed curves).
• Figure 2: $\Delta V(R)$ for the transitions involved in the Na-H$_2$ line satellite (blue curve) and K-H$_2$ satellite (red curve).
• Figure 3: Absorption cross section, $\sigma$, of the $D$2 component of the resonance lines of Na (blue curves ) and K (red curves) perturbed by H$_2$ collisions at $T = 1000$ K for $n_{\mathrm{H}_2} = 1.2 \times 10^{22}$ (full lines) and $1.8 \times 10^{22}$ cm$^{-3}$ (dotted lines). The Lorentzian approximation is overplotted for comparison (dashed curves). $\Delta\omega$ is relative to the unperturbed atomic line in cm$^{-1}$, and comparable to the energy difference $\Delta V$ of Fig. \ref{['fig:potdiff']} in the same units.
• Figure 4: The full width at half maximum (solid line) and shift (dashed line) of the Na (red) and K (blue) $D$2 spectral lines as a function of H$_2$ density. The impact approximation FWHM (dotted line) shown for comparison is invalid for all but the lowest densities.